Saddlepoint Approximation Reliability Method for Quadratic Functions in Normal Variables


If the state of a component can be predicted by a limit-state function, the First and Second Order Reliability Methods are commonly used to calculate the reliability of the component. The latter method is more accurate because it approximates the limit-state function with a quadratic form in standard normal variables. To further improve the accuracy, this study develops a saddlepoint approximation reliability method that does not require additional transformations and approximations on the quadratic function. Analytical equations are derived for the cumulant generating function (CGF) of the limit-state function in standard normal variables, and then the saddlepoint is found by equating the derivative of the CGF to the limit state. Thereafter a closed form solution to the reliability is available. The method can also apply to general nonlinear limit-state functions after they are approximated by a second order Taylor expansion. Examples show the better accuracy than the traditional second order reliability methods.


Mechanical and Aerospace Engineering

Research Center/Lab(s)

Intelligent Systems Center


This material is based in part upon the work supported by the National Science Foundation under Grant Number CMMI 1562593.

Keywords and Phrases

Number theory, Analytical equations; Closed form solutions; Cumulant generating functions; Limit state functions; Reliability methods; Saddle-point approximation; Second-order reliability methods; Second-order Taylor expansion, Reliability

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Article - Journal

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© 2018 Elsevier B.V., All rights reserved.

Publication Date

01 Mar 2018